25 citations · 96 across the 18 of their papers we have counts for
19 papers
Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. II. Dynamics
Jerry Bona, Angel Duran, Dimitrios Mitsotakis
Considered here are two systems of equations modeling the two-way propagation of long-crested, long-wavelength internal waves along the interface of a two-layer system of fluids in…
Notes on numerical analysis and solitary wave solutions of Boussinesq/Boussinesq systems for internal waves
V. A. Dougalis, A. Duran, L. Saridaki
In this paper a three-parameter family of Boussinesq systems is studied. The systems have been proposed as models of the propagation of long internal waves along the interface of a…
An asymptotic model for internal capillary-gravity waves in deep water
A. Durán
Considered in this paper is a bi-directional model for the propagation of interfacial capillary-gravity waves in a two-layer system of fluids with rigid lid condition for the upper…
On a model for internal waves in rotating fluids
A. Durán
In this paper a rotating two-fluid model for the propagation of internal waves is introduced. The model can be derived from a rotating-fluid problem by including gravity effects or…
On nonparaxial nonlinear Schrödinger-type equations
B. Cano, A. Durán
In this paper the one-dimensional nonparaxial nonlinear Schrödinger equation is considered. This was proposed as an alternative to the classical nonlinear Schrödinger equation in t…
Semidiscrete approximation to Benjamin-type equations
Vassilios A. Dougalis, Angel Duran
In this paper a semidiscrete Fourier pseudospectral method for approximating Benjamin-type equations is introduced and analyzed. A study of convergence is presented.
Numerical approximation to Benjamin type equations. Generation and stability of solitary waves
Vassilios A. Dougalis, Angel Duran, Dimitrios Mitsotakis
This paper is concerned with the study, by computational means, of the generation and stability of solitary-wave solutions of generalized versions of the Benjamin equation. The num…
An efficient method to compute solitary wave solutions of fractional Korteweg-de Vries equations
A. Duran
Considered here is an efficient technique to compute approximate profiles of solitary wave solutions of fractional Korteweg-de Vries equations. The numerical method is based on a f…
Cross-diffusion systems for image processing: II. The nonlinear case
A. Araújo, S. Barbeiro, E. Cuesta +1
In this paper the use of nonlinear cross-diffu\-sion systems to model image restoration is investigated, theoretically and numerically. In the first case, well-posedness, scale-spa…
Cross-diffusion systems for image processing: I. The linear case
A. Araujo, S. Barbeiro, E. Cuesta +1
The use of cross-diffusion systems as mathematical models of different image processes is investigated. The present paper is concerned with linear filtering. First, those systems s…
Efficient computation of capillary-gravity generalized solitary waves
Denys Dutykh, Didier Clamond, Angel Duran
This paper is devoted to the computation of capillary-gravity solitary waves of the irrotational incompressible Euler equations with free surface. The numerical study is a continua…
Numerical generation of periodic traveling wave solutions of some nonlinear dispersive wave equations
J. Alvarez, A. Duran
Proposed in this paper is a numerical procedure to generate periodic traveling wave solutions of some nonlinear dispersive wave equations. The method is based on a suitable modific…
On Petviashvili type methods for traveling wave computations: Acceleration techniques
J. Alvarez, A. Duran
In this paper a family of fixed point algorithms, generalizing the \PM method, is considered. A previous work studied the convergence of the methods. Presented here is a second par…
A plethora of generalised solitary gravity-capillary water waves
Didier Clamond, Denys Dutykh, Angel Duran
The present study describes, first, an efficient algorithm for computing capillary-gravity solitary waves solutions of the irrotational Euler equations with a free surface and, sec…
Petviashvili type methods for traveling wave computations: I. Analysis of convergence
J. Alvarez, A. Duran
In this paper a family of fixed point algorithms for the numerical resolution of some systems of nonlinear equations is designed and analyzed. The family introduced here generalize…
An extended Petviashvili method for the numerical generation of traveling and localized waves
J. Alvarez, A. Duran
A family of fixed-point iterations is proposed for the numerical computation of traveling waves and localized ground states. The methods are extended versions of Petviashvili type,…
Numerical resolution of algebraic equations with symmetries
J. Alvarez, A. Duran
Studied here is the effect of the presence of symmetry groups in a system of algebraic equations on the numerical resolution with fixed-point algorithms. It is proved that the symm…
On the Galilean invariance of some dispersive wave equations
Angel Duran, Denys Dutykh, Dimitrios Mitsotakis
Surface water waves in ideal fluids have been typically modeled by asymptotic approximations of the full Euler equations. Some of these simplified models lose relevant properties o…
Nonlinear Bloch modes, optical switching and Bragg solitons in tightly coupled micro-ring resonator chains
P. Chamorro-Posada, P. Martín-Ramos, J. Sánchez-Curto +4
We study nonlinear wave phenomena in coupled ring resonator optical waveguides in the tight coupling regime. A discrete model for the system dynamics is put forward and its steady…